PDA_DBSQAD - Integral of a B-spline using the B-representation.

Origin

SLATEC / CAMSUN

Implementation Status:

The routine and its subsidiaries will now return an error status as supplied by PDA_XERMSG.

      SUBROUTINE PDA_DBSQAD (T, BCOEF, N, K, X1, X2, BQUAD, WORK, STATUS)


***BEGIN PROLOGUE  PDA_DBSQAD
***PURPOSE  Compute the integral of a K-th order B-spline using the
            B-representation.
***LIBRARY   SLATEC
***CATEGORY  H2A2A1, E3, K6
***TYPE      DOUBLE PRECISION (BSQAD-S, PDA_DBSQAD-D)
***KEYWORDS  INTEGRAL OF B-SPLINES, QUADRATURE
***AUTHOR  Amos, D. E., (SNLA)
***DESCRIPTION

     Abstract    **** a double precision routine ****

         PDA_DBSQAD computes the integral on (X1,X2) of a K-th order
         B-spline using the B-representation (T,BCOEF,N,K).  Orders
         K as high as 20 are permitted by applying a 2, 6, or 10
         point Gauss formula on subintervals of (X1,X2) which are
         formed by included (distinct) knots.

         If orders K greater than 20 are needed, use DBFQAD with
         F(X) = 1.

         The maximum number of significant digits obtainable in
         PDA_DBSQAD is the smaller of 18 and the number of digits
         carried in double precision arithmetic.

     Description of Arguments
         Input      T,BCOEF,X1,X2 are double precision
           T      - knot array of length N+K
           BCOEF  - B-spline coefficient array of length N
           N      - length of coefficient array
           K      - order of B-spline, 1 .LE. K .LE. 20
           X1,X2  - end points of quadrature interval in
                    T(K) .LE. X .LE. T(N+1)

         Output     BQUAD,WORK are double precision
           BQUAD  - integral of the B-spline over (X1,X2)
           WORK   - work vector of length 3*K
           STATUS - Returned error status.
                    The status must be zero on entry. This
                    routine does not check the status on entry.

     Error Conditions
         Improper input is a fatal error

***REFERENCES  D. E. Amos, Quadrature subroutines for splines and
                 B-splines, Report SAND79-1825, Sandia Laboratories,
                 December 1979.
***ROUTINES CALLED  PDA_DBVALU, PDA_DINTRV, PDA_XERMSG
***REVISION HISTORY  (YYMMDD)
   800901  DATE WRITTEN
   890531  Changed all specific intrinsics to generic.  (WRB)
   890531  REVISION DATE from Version 3.2
   891214  Prologue converted to Version 4.0 format.  (BAB)
   900315  CALLs to XERROR changed to CALLs to PDA_XERMSG.  (THJ)
   900326  Removed duplicate information from DESCRIPTION section.
           (WRB)
   920501  Reformatted the REFERENCES section.  (WRB)
   950403  Implement status.  (HME)
***END PROLOGUE  PDA_DBSQAD

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